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We investigate the constraints on total neutrino mass in the scenario ofvacuum energy interacting with cold dark matter. We focus on two typicalinteraction forms, i.e., $Q=\beta H\rho_{\rm c}$ and $Q=\beta H\rho_{\Lambda}$.To avoid the occurrence of large-scale instability in interacting dark energycosmology, we adopt the parameterized post-Friedmann approach to calculate theperturbation evolution of dark energy. We employ observational data, includingthe Planck cosmic microwave background temperature and polarization data,baryon acoustic oscillation data, a JLA sample of type Ia supernovaeobservation, direct measurement of the Hubble constant, and redshift spacedistortion data. We find that, compared with those in the $\Lambda$CDM model,much looser constraints on $\sum m_{\nu}$ are obtained in the $Q=\betaH\rho_{\rm c}$ model, whereas slightly tighter constraints are obtained in the$Q=\beta H\rho_{\Lambda}$ model. Consideration of the possible mass hierarchiesof neutrinos reveals that the smallest upper limit of $\sum m_{\nu}$ appears inthe degenerate hierarchy case. By comparing the values of $\chi^2_{\rm min}$,we find that the normal hierarchy case is favored over the inverted one. Inparticular, we find that the difference $\Delta \chi^2_{\rm min} \equiv\chi^2_{\rm IH; min}-\chi^2_{\rm NH; min}> 2$ in the $Q=\beta H\rho_{\rm c}$model. In addition, we find that $\beta=0$ is consistent with the currentobservations in the $Q=\beta H\rho_{\rm c}$ model, and $\beta < 0$ is favoredat more than the $1\sigma$ level in the $Q=\beta H\rho_{\Lambda}$ model.

Exploring neutrino mass and mass hierarchy in the scenario of vacuum energy interacting with cold dark matter